I filled tower garden 2 weeks ago and added nutrients. But, we have had long periods of rain and my tower garden reservoir has remained full. I don't know how much rain has entered the reservoir. Would it be best to drain reservoir and add nutrients or to just add maybe half nutrients and see how the plants do?

From what I know, its best to put something suspended over top so it doesn't get rain in the reservoir. Other than that, definitely purchase a PPM meter (do the researc, I got mine from Amazon for $22) and Check the levels. If the reservior is below 700-800 ppm, add some nutrients. If it's between 800-1400 ppm, you're probably good.